{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 凯利公式与扔骰子"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 本文以扔硬币为例，在给定概率和盈亏比情况下，通过模拟验证了根据凯利公式确定的下注比率为最优。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.mlab as mlab\n",
    "import datetime\n",
    "from collections import defaultdict\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as plt\n",
    "sns.set_style('darkgrid')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 凯利公式 $f = \\frac{b·p - q}{b}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 用户参数设置"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# b为赔率\n",
    "b = 1.001\n",
    "# p为猜对的概率\n",
    "p = 0.52\n",
    "# q为猜错的概率\n",
    "q = 1-p\n",
    "# N为总模拟次数\n",
    "N = 1000\n",
    "# Nround为每次模拟掷硬币的次数\n",
    "Nround = 10000\n",
    "# 初始资金\n",
    "init_balance = 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 根据凯利公式计算最优下注比率\n",
    "optimalRatio = (b * p - q)/b\n",
    "\n",
    "ratio_list = [optimalRatio / 4.0, optimalRatio/ 2.0, optimalRatio*2.0, optimalRatio*4.0]\n",
    "#ratio_list = np.delete(ratio_list, [int(3.0-1)])\n",
    "\n",
    "optimal_balance = np.zeros(Nround + 1)\n",
    "ratio_balance = {}\n",
    "for tmpratio in ratio_list:\n",
    "    ratio_balance[tmpratio] = np.zeros(Nround + 1)\n",
    "\n",
    "optimalbalance = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(N):\n",
    "#     print i\n",
    "    # 生成随机数\n",
    "    draws = np.random.uniform(0, 1, Nround)\n",
    "\n",
    "    # 初始资金\n",
    "    cur_balance = init_balance\n",
    "    balance_list = [init_balance]\n",
    "\n",
    "    # balance_dic保存不同ratio下的资金\n",
    "    balance_dic = defaultdict(list)\n",
    "    for tmpratio in ratio_list:\n",
    "        balance_dic[tmpratio].append(init_balance)\n",
    "\n",
    "    for draw in draws:\n",
    "        if draw <= p:\n",
    "            # 猜对\n",
    "            cur_balance += cur_balance * optimalRatio * b\n",
    "            balance_list.append(cur_balance)\n",
    "            for tmpratio in ratio_list:\n",
    "                tmpbalance = balance_dic[tmpratio][-1]\n",
    "                tmpbalance += tmpbalance * tmpratio * b\n",
    "                balance_dic[tmpratio].append(tmpbalance)\n",
    "        else:\n",
    "            # 猜错\n",
    "            cur_balance -= cur_balance * optimalRatio\n",
    "            balance_list.append(cur_balance)\n",
    "            for tmpratio in ratio_list:\n",
    "                tmpbalance = balance_dic[tmpratio][-1]\n",
    "                tmpbalance -= tmpbalance * tmpratio\n",
    "                balance_dic[tmpratio].append(tmpbalance)\n",
    "    \n",
    "#     print balance_list[-1]\n",
    "    \n",
    "    optimal_balance += np.array(balance_list)\n",
    "\n",
    "    for tmpratio in ratio_list:\n",
    "        ratio_balance[tmpratio] += np.array(balance_dic[tmpratio])\n",
    "#         print balance_dic[tmpratio][-1]\n",
    "\n",
    "optimal_balance /= N\n",
    "for tmpratio in ratio_list:\n",
    "    ratio_balance[tmpratio] /= N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 设置画图颜色\n",
    "colormap = [(31, 119, 180) , (174, 199, 232) , (255, 127, 14)  , (255, 187, 120), \n",
    "            (44, 160, 44)  , (152, 223, 138) , (148, 103, 189) , (197, 176, 213), \n",
    "            (214, 39, 40)  , (255, 152, 150) , (140, 86, 75)   , (196, 156, 148),  \n",
    "            (227, 119, 194), (247, 182, 210) , (127, 127, 127) , (199, 199, 199),  \n",
    "            (188, 189, 34) , (219, 219, 141) , (23, 190, 207)  , (158, 218, 229)]  \n",
    "\n",
    "for i in range(len(colormap)):  \n",
    "    r, g, bb = colormap[i]  \n",
    "    colormap[i] = (r / 255., g / 255., bb / 255.)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x987f588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 画图\n",
    "fig, ax1 = plt.subplots(figsize=(18, 9))\n",
    "ax1.plot(balance_list, color = 'blue', label = 'Optimal : %.3f' % optimalRatio, linewidth = 0.8, alpha = 0.8)\n",
    "for i in range(len(ratio_list)):\n",
    "    ax1.plot(balance_dic[ratio_list[i]], color = colormap[i], label = '%.3f' % ratio_list[i], linewidth = 0.8, alpha = 0.8)\n",
    "ax1.axhline(y = init_balance, color = 'red', linestyle = '--', linewidth = 0.8, alpha = 0.8)\n",
    "ax1.set_ylabel('Size', fontsize = 12)\n",
    "#ax1.set_yscale(\"log\")\n",
    "plt.legend(fontsize = 12)\n",
    "# ax2 = ax1.twinx()\n",
    "# ax2.plot(dateList, closeArray, color = 'red')\n",
    "# ax2.set_ylabel('Price')\n",
    "# plt.axvline(Nround / 5., c='k', ls='--')\n",
    "plt.title('Balance under different ratio', fontsize=15)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
